Internal problem ID [12292]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 10 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y=0} \] With initial conditions \begin {align*} [y^{\prime }\left (1\right ) = 3, y^{\prime }\left (2\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,D(y)(1) = 3, D(y)(2) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -x^{3}+3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 13
DSolve[{x^2*y''[x]-4*x*y'[x]+6*y[x]==0,{y'[1]==3,y'[2]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\left ((x-3) x^2\right ) \]